Darwin approximation, a non-relativistic submodel of the Maxwell's equations, has been used for theoretical and computational investigations of magnetized plasmas. In this short paper, an improved Darwin approximation is proposed, which is applicable not only to the Coulomb gauge but also to the Lorenz counterpart. The proposed approximation exactly satisfies the conservation of charge, momentum, and energy under the use of the Lorenz and Coulomb gauges.

1.
C. G.
Darwin
, “
LI. The dynamical motions of charged particles
,”
London, Edinburgh Dublin Philos. Mag. J. Sci.
39
,
537
551
(
1920
).
2.
A. N.
Kaufman
and
P. S.
Rostler
, “
The Darwin model as a tool for electromagnetic plasma simulation
,”
Phys. Fluids
14
,
446
448
(
1971
).
3.
B. B.
Godfrey
, “
Numerical Cherenkov instabilities in electromagnetic particle codes
,”
J. Comput. Phys.
15
,
504
521
(
1974
).
4.
M. R.
Gibbons
and
D. W.
Hewett
, “
The Darwin direct implicit particle-in-cell (DADIPIC) method for simulation of low frequency plasma phenomena
,”
J. Comput. Phys.
120
,
231
247
(
1995
).
5.
H.
Schmitz
and
R.
Grauer
, “
Darwin–Vlasov simulations of magnetised plasmas
,”
J. Comput. Phys.
214
,
738
756
(
2006
).
6.
M.
Seehafer
, “
Global classical solutions of the Vlasov–Darwin system for small initial data
,”
Commun. Math. Sci.
6
,
749
764
(
2008
).
7.
G.
Chen
and
L.
Chacón
, “
An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov–Darwin particle-in-cell algorithm
,”
Comput. Phys. Commun.
185
,
2391
2402
(
2014
).
8.
G.
Chen
and
L.
Chacón
, “
A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm
,”
Comput. Phys. Commun.
197
,
73
87
(
2015
).
9.
O.
Pezzi
,
G.
Cozzani
,
F.
Califano
,
F.
Valentini
,
M.
Guarrasi
,
E.
Camporeale
,
G.
Brunetti
,
A.
Retinò
, and
P.
Veltri
, “
ViDA: A Vlasov–DArwin solver for plasma physics at electron scales
,”
J. Plasma Phys.
85
,
905850506
(
2019
).
10.
T. B.
Krause
,
A.
Apte
, and
P. J.
Morrison
, “
A unified approach to the Darwin approximation
,”
Phys. Plasmas
14
,
102112
(
2007
).
11.
A.
Hasegawa
and
H.
Okuda
, “
One-dimensional plasma model in the presence of a magnetic field
,”
Phys. Fluids
11
,
1995
2003
(
1968
).
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